On 2011.05.30. 12:33, Ben wrote:
> I'd like to compile a function that estimates (assuming a spherical
> earth) the length of a degree of longitude at any particular
> latitude. Here's how I write it up and test its speed:
>
> In[1]:= radiusOfEarth=6378100.;
> latitudeDegreeLength=2*Pi*radiusOfEarth/360
> Out[2]= 111319.
> In[3]:= X=Table[RandomReal[{0,90}],{100000}];
> In[4]:=
> GetLongitudeDegreeLength=Compile[{latitude},latitudeDegreeLength*Cos[latitude
> Degree]]
> Out[4]= CompiledFunction[{latitude},latitudeDegreeLength Cos[latitude
> =B0],-CompiledCode-]
> In[5]:= Timing[Map[GetLongitudeDegreeLength,X];]
> Out[5]:= {0.312,Null}
>
> Since the values of "latitudeDegreeLength" and "Degree" are constant,
> I'd prefer to use numerical approximations in the definition so the
> compiled code doesn't have to request the values of these global
> variables at runtime. Like this:
>
> In[6]:= GetLongitudeDegreeLength=Compile[{latitude},
> 111318.*Cos[0.0174532925 latitude]]
> Out[6]:= CompiledFunction[{latitude},111318. Cos[0.0174533 latitude],-
> CompiledCode-]
> In[7]:= Timing[Map[GetLongitudeDegreeLength,X];]
> Out[7]:= {0.031,Null}
>
> Is there any way to tell Mathematica that I'd like these symbols to be
> evaluated before the compilation so that I don't have to copy and
> paste the numerical values into the definition?
>
After reading up a bit more on Compile[] based on Oliver's replies, I
came across another possible solution, which you might find interesting:
GetLongitudeDegreeLength =
Compile[{{latitude, _Integer, 0}},
latitudeDegreeLength*Cos[latitude Degree],
CompilationOptions -> {"InlineExternalDefinitions" -> True}]
This is documented at ref/CompilationOptions and
Compile/tutorial/Operation
-- Szabolcs